We consider the equation F (x) + (x) =y. Here F \, Rⁿ Rᵐ is a nonlinear smooth mapping, x is the unknown, is a continuous mapping, and y is a vector. Using -truncations we obtain conditions for the equation to have a solution x (y, ) close to a given point x. The perturbation is assumed to be sufficiently small in a given neighborhood of x in the uniform metric, and the perturbation y is assumed to be close to F (x). We also derive a priori estimates for the solution x (y, ).
Arutyunov et al. (Fri,) studied this question.
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